Semiotics as an analytic tool for the didactics of mathematics

This paper is a theoretical analysis of (what the author perceives to be) one of the most exciting and promising directions in research on the didactics of mathematics: studying the learning of mathematics as the initiation to, and internalisation of, certain semiotic systems. Three principal ways in which this point of view can contribute crucially to didactical research are presented and exemplified; they concern the cognitive, social and cultural aspects of mathematics education. Finally, as a topic transcending the three aspects, we consider the use of digital semiotic appliances in mathematics teaching; some results from research in this new area are outlined.